Biomedical engineering, particularly as it applies to neuroscience, has reached a stage of development at which further understanding of complex neural systems, such as the hippocampus and other cortical regions that underlie cognition and higher thought processes, will depend on mathematical modeling as a means to organize experimental data that is known, and to systematically explore the unknown. The research objectives of Core Project #4 are to further develop and apply methodologies based on principles of nonlinear systems theory for experimentally-based, mathematical modeling of neurons and neural systems. This approach leads to what are commonly termed non-parametric or input-output models, i.e., functional properties that emerge as a consequence of interactions among the internal components of the system - without necessarily describing the internal components themselves. In contrast, parametric models represent the mechanistic properties of the system, with parameters that can be interpreted directly with respect to those underlying mechanisms. We will explore parametric modeling of the hippocampus both in the context of a glutamatergic synaptic model (EONS) continued from previous work, and a new project: a large-scale, compartmental neuron model (10[6] neurons, 10[10] synapses) of hippocampus that incorporates much of the quantitative neuroanatomy, synaptic physiology, and topographic connectivity available for that structure. Ultimately our goal is to establish means for the synergistic use of non-parametric and parametric modeling methods, in the context of accelerating multi-scale modeling, to further our understanding of how global system dynamics underlying cognition, and specifically memory, derive from molecular and synaptic mechanisms.